Fluctuating periodic solutions and moment boundedness of a stochastic model for the bone remodeling process

Saúl Díaz Infante Velasco, Silvia Jerez, Benito Chen-Charpentier

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this work, we model osteoclast-osteoblast population dynamics with random environmental fluctuations in order to understand the random variations of the bone remodeling process in real life. For this purpose, we construct a stochastic differential model for the interactions between the osteoclast and osteoblast cell populations using the parameter perturbation technique. We prove the existence of a globally attractive positive unique solution for the stochastically perturbed system. Also, the stochastic boundedness of the solution is demonstrated using its p-th order moments for p ≥ 1. Finally, we show that the introduction of noise in the deterministic model provides a fluctuating periodic solution. Numerical evidence supports our theoretical results and a discussion of the results is carried out.
Original languageSpanish (Mexico)
Pages (from-to)153
Number of pages164
JournalMathematical Biosciences
Volume299
DOIs
StatePublished - 8 Mar 2018

Cite this

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title = "Fluctuating periodic solutions and moment boundedness of a stochastic model for the bone remodeling process",
abstract = "In this work, we model osteoclast-osteoblast population dynamics with random environmental fluctuations in order to understand the random variations of the bone remodeling process in real life. For this purpose, we construct a stochastic differential model for the interactions between the osteoclast and osteoblast cell populations using the parameter perturbation technique. We prove the existence of a globally attractive positive unique solution for the stochastically perturbed system. Also, the stochastic boundedness of the solution is demonstrated using its p-th order moments for p ≥ 1. Finally, we show that the introduction of noise in the deterministic model provides a fluctuating periodic solution. Numerical evidence supports our theoretical results and a discussion of the results is carried out.",
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Fluctuating periodic solutions and moment boundedness of a stochastic model for the bone remodeling process. / Díaz Infante Velasco, Saúl; Jerez, Silvia; Chen-Charpentier, Benito.

In: Mathematical Biosciences, Vol. 299, 08.03.2018, p. 153.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Fluctuating periodic solutions and moment boundedness of a stochastic model for the bone remodeling process

AU - Díaz Infante Velasco, Saúl

AU - Jerez, Silvia

AU - Chen-Charpentier, Benito

PY - 2018/3/8

Y1 - 2018/3/8

N2 - In this work, we model osteoclast-osteoblast population dynamics with random environmental fluctuations in order to understand the random variations of the bone remodeling process in real life. For this purpose, we construct a stochastic differential model for the interactions between the osteoclast and osteoblast cell populations using the parameter perturbation technique. We prove the existence of a globally attractive positive unique solution for the stochastically perturbed system. Also, the stochastic boundedness of the solution is demonstrated using its p-th order moments for p ≥ 1. Finally, we show that the introduction of noise in the deterministic model provides a fluctuating periodic solution. Numerical evidence supports our theoretical results and a discussion of the results is carried out.

AB - In this work, we model osteoclast-osteoblast population dynamics with random environmental fluctuations in order to understand the random variations of the bone remodeling process in real life. For this purpose, we construct a stochastic differential model for the interactions between the osteoclast and osteoblast cell populations using the parameter perturbation technique. We prove the existence of a globally attractive positive unique solution for the stochastically perturbed system. Also, the stochastic boundedness of the solution is demonstrated using its p-th order moments for p ≥ 1. Finally, we show that the introduction of noise in the deterministic model provides a fluctuating periodic solution. Numerical evidence supports our theoretical results and a discussion of the results is carried out.

KW - Bone remodeling Stochastic differential equations Brownian motion Moment boundedness Fluctuating periodic solution Osteoclasts Osteoblasts

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